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# 138assgn8 - MATH 138 Assignment 8 Series(part III Power...

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MATH 138 Assignment 8 Spring 2009 Series (part III). Power series. Submit all problems marked (*) and the Maple Lab 4 by 12:30 p.m. on Friday, July 10. 1. ( * ) Determine whether the series is absolutely convergent, conditionally convergent or divergent. (a) n =1 n 2 2 n (b) n =1 ( - 1) n - 1 2 n n 4 (c) n =1 n ! 100 n (d) n =1 ( - 1) n n n 3 +2 (e) n =1 sin(4 n ) 4 n (f) n =1 3 - cos n n 2 / 3 - 2 (g) n =1 ( - 1) n ln n (h) 2 5 + 2 · 6 5 · 8 + 2 · 6 · 10 5 · 8 · 11 + 2 · 6 · 10 · 14 5 · 8 · 11 · 14 + · · · 2. ( * ) The general terms of a series are defined recursively by a 1 = 2, a n +1 = 5 n +1 4 n +3 a n . Determine whether a n converges or not. 3. The general terms of a series are defined recursively by a 1 = 1, a n +1 = 2+cos n n a n . Determine whether a n converges or not. 4. Find the positive integers k for which the series n =1 ( n !) 2 ( kn )! is convergent. 5. ( * ) Show that n =0 x n n ! converges for all x . Deduce that lim n →∞ x n n !

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138assgn8 - MATH 138 Assignment 8 Series(part III Power...

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